Eldritch blast is a spell-like ability, which means it cannot be cast while the warlock is within the antimagic field, and the beam itself is suppressed within the field, so it cannot hit a target within the field. As normal, the blast is not blocked by the field, so a warlock outside the field could cast eldritch blast through the field to get a target on the far side of it.
Hellfire blast does not change any of this.
Vitriolic blast is a greater eldritch essence invocation, and converts eldritch blast to an SR: No acid-damage conjuration. It isn’t specifically called out, but instantaneous SR: No conjuration (creation) spells like acid splash can be cast into antimagic field by a caster outside of it. The logic here is that the magic creates and propels some physical substance, like acid, from there after it’s just physics and chemistry—nothing antimagic field can interfere with. I have always rules that vitriolic blast operates in the same manner and has the same benefit. And every warlock with greater invocations and any interest in blasting should have vitriolic blast, regardless of your ruling, for dealing with SR.
Anyway, it’s not immediately clear whether you can apply hellfire blast and vitriolic blast at the same time, or what happens if you do. Certainly, hellfire blast sounds similar to an eldritch essence, but it never actually says it is one or that you cannot also use one on the hellfire blast. But even if you do, can vitriolic blast turn hellfire into acid? Does it still deal the extra damage if you do? Officially, the answer is “yes,” because nothing nixes that combination and ordering, but it’s worth thinking about.
Finally, a note on balance—the warlock class is vastly weaker than anyone who can cast antimagic field. Be careful about trying to counter the warlock in the name of “balance”—it is already on the weaker side. That said, casting antimagic field is almost-always a self-nerf—it covers a small area, which must include you, who by definition are a high-level spellcaster. Your enemies can easily stand outside it and pelt you with arrows, or those aforementioned instantaneous SR: No creation spells.
But all of that is irrelevant because 4th-level characters cannot meaningfully play the game alongside or in opposition to 15th-level characters. Actually, they’d have a really hard time contributions meaningfully with or against 7th-level characters, and you want to more than double that. This will not be an encounter, this will be a cutscene. Which, in my opinion, doesn’t make got a great gaming experience, though YMMV.